Problem

The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. Find the mean, median, mode, and standard deviation. Round to one decimal place as needed. $19,22,25,27,30,32,35,35$ Mean $=$ Median = Mode $=$ Standard Deviation $=$

Solution

Step 1 :Calculate the mean by adding all the numbers and dividing by the count of numbers: \(\frac{19+22+25+27+30+32+35+35}{8} = \frac{225}{8} = 28.1\)

Step 2 :Find the median by listing the numbers in order and finding the middle number. Since there are 8 numbers, the median is the mean of the 4th and 5th numbers: \(\frac{27+30}{2} = 28.5\)

Step 3 :Identify the mode as the number that appears most frequently. In this case, the number 35 appears twice, more than any other number: \(\boxed{35}\)

Step 4 :Calculate the standard deviation by first finding the differences from the mean: \(19-28.1 = -9.1, 22-28.1 = -6.1, 25-28.1 = -3.1, 27-28.1 = -1.1, 30-28.1 = 1.9, 32-28.1 = 3.9, 35-28.1 = 6.9, 35-28.1 = 6.9\)

Step 5 :Square these differences: \(82.81, 37.21, 9.61, 1.21, 3.61, 15.21, 47.61, 47.61\)

Step 6 :Find the mean of these squared differences: \(\frac{82.81+37.21+9.61+1.21+3.61+15.21+47.61+47.61}{8} = 30.6\)

Step 7 :Take the square root of this number to find the standard deviation: \(\sqrt{30.6} = \boxed{5.5}\)

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Source: https://solvelyapp.com/problems/LMzSYYobLt/

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